Report of the fit

Fit summary

Description: PV19 version x, parameters for NNLL. Initial parameters from a previous fit with ceres on replica zero. T0 parameters from the previous to previous fit. Steps from minuit minimisation.
Minimiser: minuit
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Cut on the error function: 4
Parameterisation: PV19x
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2 N_1 \alpha \sigma \lambda N_{1B} \alpha_B \sigma_B g_{2B}
0.005144 0.68535248 0.21943481 0.3329461 0.66627605 0.0387879 0.075758463 0.34845635 0.019224141

Theory summary

Collinear PDF set: MMHT2014nlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: NNLL
Initial parameters fluctuations: True
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 173
\chi_{0}^2 = 1.6571
\chi_{mean}^2 = 1.6341
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.6823 \pm 0.0163
\langle E \rangle \pm \sigma_{E} = 2.6372 \pm 0.1915

Parameters

Parameter Central replica Average over replicas Fixed
g_2 -0.091343204 -0.09242544 \pm 0.01642545 False
N_1 5.3553982 5.3553982 \pm 0.0 True
\alpha 1.0805391 1.09779861 \pm 0.38066408 False
\sigma 0.9431266 0.91765216 \pm 0.12484923 False
\lambda 0.49120348 0.48996388 \pm 0.07100341 False
N_{1B} 0.040471695 0.04404218 \pm 0.01034721 False
\alpha_B 0.052405509 0.05811231 \pm 0.02975318 False
\sigma_B 0.56591202 0.53112528 \pm 0.11609349 False
g_{2B} 0.034188315 0.03495914 \pm 0.00804642 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha distribution
\sigma distribution
\lambda distribution
N_{1B} distribution
\alpha_B distribution
\sigma_B distribution
g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4826 0.0313 0.514
E605_Q_8_9 8 0.9991 0.0179 1.017
E605_Q_10.5_11.5 10 0.4928 0.1393 0.6322
E288_200_Q_4_5 4 0.9256 0.8564 1.782
E288_200_Q_5_6 5 2.3052 0.3541 2.6593
E288_200_Q_6_7 6 0.7917 0.2111 1.0028
E288_200_Q_7_8 7 0.9857 0.032 1.0177
E288_200_Q_8_9 8 0.7347 0.0059 0.7406
E288_300_Q_4_5 4 0.7749 0.3398 1.1147
E288_300_Q_5_6 5 1.394 0.0995 1.4935
E288_300_Q_6_7 6 1.0371 0.0397 1.0768
E288_300_Q_7_8 7 0.3419 0.0425 0.3844
E288_300_Q_8_9 8 0.3924 0.0384 0.4308
E288_400_Q_5_6 5 0.9363 0.0011 0.9374
E288_400_Q_6_7 6 0.5219 0.0069 0.5287
E288_400_Q_7_8 7 0.2461 0.0139 0.26
E288_400_Q_8_9 8 0.5589 0.0127 0.5716
E288_400_Q_11_12 11 0.5713 0.0068 0.5781
E288_400_Q_12_13 12 0.5368 0.0113 0.5481
E288_400_Q_13_14 12 0.3425 0.0362 0.3787
STAR_510 7 1.193 0.0135 1.2066
CDF_RunI 25 0.6526 0.1483 0.8009
CDF_RunII 26 1.2796 0.0074 1.287
D0_RunI 12 0.6669 0.0018 0.6687
D0_RunII 5 0.914 0.2909 1.2049
D0_RunIImu 3 0.1228 0.0862 0.2089
LHCb_7TeV 7 1.9434 0.8425 2.7859
LHCb_8TeV 7 1.9152 1.452 3.3672
LHCb_13TeV 7 1.4916 0.2891 1.7807
CMS_7TeV 4 2.8935 0 2.8935
CMS_8TeV 4 1.4855 0.1783 1.6639
ATLAS_7TeV_y_0_1 6 6.9605 1.0906 8.0511
ATLAS_7TeV_y_1_2 6 4.9357 0.4829 5.4186
ATLAS_7TeV_y_2_2.4 6 1.8106 0.0099 1.8206
ATLAS_8TeV_y_0_0.4 6 4.7809 0.9768 5.7576
ATLAS_8TeV_y_0.4_0.8 6 6.7037 1.5463 8.2501
ATLAS_8TeV_y_0.8_1.2 6 4.364 0.6694 5.0335
ATLAS_8TeV_y_1.2_1.6 6 2.9492 0.4253 3.3745
ATLAS_8TeV_y_1.6_2 6 2.5631 0.2704 2.8336
ATLAS_8TeV_y_2_2.4 6 1.2871 0.162 1.449
ATLAS_8TeV_Q_46_66 4 0.7702 0.0369 0.8071
ATLAS_8TeV_Q_116_150 8 1.1515 0.0073 1.1587
Total 319 - - 1.6571
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.6195 0.0842 0.7037
E605_Q_8_9 8 1.2033 0.0491 1.2524
E605_Q_10.5_11.5 10 0.3704 0.0966 0.467
E288_200_Q_4_5 4 0.4592 0.4626 0.9218
E288_200_Q_5_6 5 1.3421 0.2805 1.6226
E288_200_Q_6_7 6 0.5894 0.1838 0.7731
E288_200_Q_7_8 7 0.9044 0.0379 0.9423
E288_200_Q_8_9 8 0.9133 0.009 0.9223
E288_300_Q_4_5 4 0.5417 0.1742 0.7159
E288_300_Q_5_6 5 1.1792 0.0622 1.2414
E288_300_Q_6_7 6 0.9837 0.0266 1.0104
E288_300_Q_7_8 7 0.3435 0.0331 0.3766
E288_300_Q_8_9 8 0.2798 0.0403 0.3201
E288_400_Q_5_6 5 1.1387 0.0151 1.1538
E288_400_Q_6_7 6 0.6721 0.0307 0.7028
E288_400_Q_7_8 7 0.3372 0.0486 0.3857
E288_400_Q_8_9 8 0.7678 0.0428 0.8106
E288_400_Q_11_12 11 0.843 0.0125 0.8555
E288_400_Q_12_13 12 0.8667 0.0144 0.8812
E288_400_Q_13_14 12 0.8896 0.0579 0.9475
STAR_510 7 1.1585 0.0374 1.1959
CDF_RunI 25 0.5704 0.1422 0.7126
CDF_RunII 26 1.2159 0.006 1.2219
D0_RunI 12 0.6306 0.0007 0.6313
D0_RunII 5 1.0627 0.2934 1.3561
D0_RunIImu 3 0.0272 0.0358 0.063
LHCb_7TeV 7 1.661 0.8488 2.5097
LHCb_8TeV 7 1.7915 1.3835 3.175
LHCb_13TeV 7 1.344 0.2686 1.6126
CMS_7TeV 4 2.8712 0 2.8712
CMS_8TeV 4 1.4974 0.1813 1.6787
ATLAS_7TeV_y_0_1 6 6.8994 1.096 7.9954
ATLAS_7TeV_y_1_2 6 4.7533 0.4859 5.2392
ATLAS_7TeV_y_2_2.4 6 1.6877 0.0099 1.6977
ATLAS_8TeV_y_0_0.4 6 4.738 1.0098 5.7477
ATLAS_8TeV_y_0.4_0.8 6 6.4935 1.5968 8.0902
ATLAS_8TeV_y_0.8_1.2 6 4.3266 0.6857 5.0122
ATLAS_8TeV_y_1.2_1.6 6 2.9076 0.4354 3.3429
ATLAS_8TeV_y_1.6_2 6 2.4013 0.2642 2.6655
ATLAS_8TeV_y_2_2.4 6 1.1461 0.1525 1.2986
ATLAS_8TeV_Q_46_66 4 0.7042 0.0484 0.7526
ATLAS_8TeV_Q_116_150 8 1.1248 0.0066 1.1314
Total 319 - - 1.6341
Average-over-replicas \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4012 \pm 0.196 0.1483 \pm 0.1924 0.5495 \pm 0.0847
E605_Q_8_9 8 1.0003 \pm 0.2367 0.0859 \pm 0.1279 1.0862 \pm 0.2086
E605_Q_10.5_11.5 10 0.4673 \pm 0.2605 0.2056 \pm 0.2478 0.6728 \pm 0.0761
E288_200_Q_4_5 4 0.5306 \pm 1.2697 1.2825 \pm 1.266 1.8131 \pm 0.2217
E288_200_Q_5_6 5 2.1727 \pm 0.6684 0.4979 \pm 0.6223 2.6706 \pm 0.2632
E288_200_Q_6_7 6 0.6727 \pm 0.4411 0.3413 \pm 0.3939 1.014 \pm 0.1729
E288_200_Q_7_8 7 0.9237 \pm 0.2413 0.1062 \pm 0.1425 1.0299 \pm 0.1998
E288_200_Q_8_9 8 0.688 \pm 0.1183 0.064 \pm 0.0755 0.752 \pm 0.0997
E288_300_Q_4_5 4 0.5549 \pm 0.7565 0.5879 \pm 0.7068 1.1428 \pm 0.185
E288_300_Q_5_6 5 1.2346 \pm 0.4592 0.2725 \pm 0.3725 1.5071 \pm 0.2395
E288_300_Q_6_7 6 0.9221 \pm 0.3494 0.1676 \pm 0.2324 1.0896 \pm 0.2635
E288_300_Q_7_8 7 0.2477 \pm 0.2349 0.1536 \pm 0.1913 0.4012 \pm 0.137
E288_300_Q_8_9 8 0.3315 \pm 0.1806 0.1181 \pm 0.179 0.4496 \pm 0.0463
E288_400_Q_5_6 5 0.8122 \pm 0.3319 0.1509 \pm 0.205 0.963 \pm 0.264
E288_400_Q_6_7 6 0.4678 \pm 0.2964 0.1032 \pm 0.1282 0.571 \pm 0.2674
E288_400_Q_7_8 7 0.2127 \pm 0.269 0.1056 \pm 0.1538 0.3184 \pm 0.2222
E288_400_Q_8_9 8 0.5501 \pm 0.1788 0.0772 \pm 0.1165 0.6274 \pm 0.1502
E288_400_Q_11_12 11 0.5719 \pm 0.131 0.0414 \pm 0.055 0.6132 \pm 0.1358
E288_400_Q_12_13 12 0.5431 \pm 0.0747 0.0394 \pm 0.0527 0.5825 \pm 0.0703
E288_400_Q_13_14 12 0.3493 \pm 0.1013 0.0564 \pm 0.0544 0.4057 \pm 0.0953
STAR_510 7 1.0834 \pm 0.2123 0.1266 \pm 0.1987 1.2099 \pm 0.0741
CDF_RunI 25 0.6151 \pm 0.1782 0.1935 \pm 0.176 0.8086 \pm 0.0292
CDF_RunII 26 1.2818 \pm 0.2061 0.0594 \pm 0.0782 1.3412 \pm 0.1926
D0_RunI 12 0.606 \pm 0.118 0.0671 \pm 0.0903 0.6731 \pm 0.0658
D0_RunII 5 0.7417 \pm 0.6179 0.4881 \pm 0.5955 1.2298 \pm 0.2071
D0_RunIImu 3 -0.4071 \pm 0.6127 0.6123 \pm 0.5833 0.2052 \pm 0.148
LHCb_7TeV 7 1.7025 \pm 0.7706 1.1015 \pm 0.7533 2.8039 \pm 0.1105
LHCb_8TeV 7 1.9122 \pm 1.0007 1.5449 \pm 0.9398 3.4572 \pm 0.3265
LHCb_13TeV 7 1.4642 \pm 0.3904 0.3374 \pm 0.3847 1.8016 \pm 0.0951
CMS_7TeV 4 2.8904 \pm 0.0257 0.0 \pm 0.0 2.8904 \pm 0.0257
CMS_8TeV 4 1.3955 \pm 0.2499 0.2567 \pm 0.2426 1.6522 \pm 0.0817
ATLAS_7TeV_y_0_1 6 6.8515 \pm 0.6888 1.1929 \pm 0.5544 8.0444 \pm 0.3425
ATLAS_7TeV_y_1_2 6 4.8939 \pm 0.4218 0.5516 \pm 0.3337 5.4455 \pm 0.3158
ATLAS_7TeV_y_2_2.4 6 1.795 \pm 0.1024 0.0259 \pm 0.0376 1.8208 \pm 0.0947
ATLAS_8TeV_y_0_0.4 6 4.7816 \pm 0.5525 1.0105 \pm 0.4893 5.792 \pm 0.2334
ATLAS_8TeV_y_0.4_0.8 6 6.6527 \pm 0.7791 1.6466 \pm 0.7575 8.2993 \pm 0.2469
ATLAS_8TeV_y_0.8_1.2 6 4.2661 \pm 0.4391 0.7099 \pm 0.3556 4.976 \pm 0.1986
ATLAS_8TeV_y_1.2_1.6 6 2.8735 \pm 0.3963 0.4848 \pm 0.3412 3.3583 \pm 0.191
ATLAS_8TeV_y_1.6_2 6 2.6145 \pm 0.4707 0.3261 \pm 0.3039 2.9407 \pm 0.3556
ATLAS_8TeV_y_2_2.4 6 1.2372 \pm 0.3339 0.2317 \pm 0.221 1.4689 \pm 0.2683
ATLAS_8TeV_Q_46_66 4 0.5797 \pm 0.306 0.2128 \pm 0.303 0.7925 \pm 0.0644
ATLAS_8TeV_Q_116_150 8 1.0586 \pm 0.182 0.1009 \pm 0.1784 1.1595 \pm 0.0429
Total 319 - - 1.6823 \pm 0.0163

TMDs in k_T space

TMD PDF of the d at Q = 2 GeV and x = 0.001
TMD PDF of the d at Q = 2 GeV and x = 0.01
TMD PDF of the d at Q = 2 GeV and x = 0.1
TMD PDF of the d at Q = 2 GeV and x = 0.5
TMD PDF of the d at Q = 2 GeV and x = 0.9

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison